A complete system of partial differential equations governing three-dimensional laminar flow of an incompressible viscous neutrally charged carrier fluid injected with an electrically charged fluid has been elaborated. The model accounts for temperature dependent physical properties via an extended Boussinesq approximation while including a Joule heating effect. The system of coupled partial differential equations was solved using an artificial compressibility formulation and explicit finite differencing with a four-step Runge-Kutta time integration. Two-dimensional numerical results demonstrate a case of an electrohydrodynamic instability and several cases of bending of a stream of charged particles under the influence of an external electric field. Transformation of an initially circular domain of charged particles into oval and crescent shapes was also demonstrated with success.
